To find the equation of a line given a slope and a point through which the line passes, we use the point-slope form of a linear equation:
y - y1 = m(x - x1)
In this problem, we have the point (4,3) and the slope -1/2, so we'll substitute those into the equation:
y - 3 = -1/2(x - 4)
Before we simplify this equation, let's recall that our ultimate goal is to find y in terms of x, or to put the equation in slope-intercept form, which is:
y = mx + b
To get our equation in this form, we will need to eliminate the parentheses and the subtraction on the left side of the equation:
y - 3 = -1/2x + 2
Then, we just add 3 to both sides to isolate y:
y = -1/2x + 5
So, the equation of the line with slope -1/2 passing through the point (4,3) is y = -1/2x + 5.
We can also determine from this equation that the line intersects the y-axis at the point (0,5). This point is the y-intercept of the line, and this can be represented by b = 5 in our equation, as b is the constant term in the equation of the line in slope-intercept form, y = mx + b.
Therefore, the equation of the line is y = -1/2x + 5 and the y -intercept is b = 5.